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Stock-Based Compensation (Details 11) (Stock Appreciation Rights [Member], USD $)
In Millions, unless otherwise specified
12 Months Ended
Dec. 31, 2014
Dec. 31, 2013
Dec. 31, 2012
Stock Appreciation Rights [Member]
     
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Instrinsic value of stock appreciation rights exercised $ 27.3lii_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsExercisesInPeriodIntrinsicValue
/ us-gaap_AwardTypeAxis
= us-gaap_StockAppreciationRightsSARSMember
$ 16.7lii_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsExercisesInPeriodIntrinsicValue
/ us-gaap_AwardTypeAxis
= us-gaap_StockAppreciationRightsSARSMember
$ 14.4lii_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsExercisesInPeriodIntrinsicValue
/ us-gaap_AwardTypeAxis
= us-gaap_StockAppreciationRightsSARSMember
Realized tax benefits from tax deductions $ 10.4us-gaap_EmployeeServiceShareBasedCompensationTaxBenefitFromCompensationExpense
/ us-gaap_AwardTypeAxis
= us-gaap_StockAppreciationRightsSARSMember
$ 6.4us-gaap_EmployeeServiceShareBasedCompensationTaxBenefitFromCompensationExpense
/ us-gaap_AwardTypeAxis
= us-gaap_StockAppreciationRightsSARSMember
$ 5.5us-gaap_EmployeeServiceShareBasedCompensationTaxBenefitFromCompensationExpense
/ us-gaap_AwardTypeAxis
= us-gaap_StockAppreciationRightsSARSMember